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• Articles by Richard S. Norman

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• Synaptic Integration in Electrically Coupled Neurons

  Synaptic Integration in Electrically Coupled Neurons Biophysical Journal, Volume 86, Issue 1, 1 January 2004, Pages 646-655 Elizabeth García-Pérez, Mariana Vargas-Caballero, Norma Velazquez-Ulloa, Antonmaria Minzoni and Francisco F. De-Miguel Abstract Interactions among chemical and electrical synapses regulate the patterns of electrical activity of vertebrate and invertebrate neurons. In this investigation we studied how electrical coupling influences the integration of excitatory postsynaptic potentials (EPSPs). Pairs of Retzius neurons of the leech are coupled by a nonrectifying electrical synapse by which chemically induced synaptic currents flow from one neuron to the other. Results from electrophysiology and modeling suggest that chemical synaptic inputs are located on the coupled neurites, at 7.5m from the electrical synapses. We also showed that the space constant of the coupled neurites was 100m, approximately twice their length, allowing the efficient spread of synaptic currents all along both coupled neurites. Based on this cytoarchitecture, our main finding was that the degree of electrical coupling modulates the amplitude of EPSPs in the driving neurite by regulating the leak of synaptic current to the coupled neurite, so that the amplitude of EPSPs in the driving neurite was proportional to the value of the coupling resistance. In contrast, synaptic currents arriving at the coupled neurite through the electrical synapse produced EPSPs of constant amplitude. This was because the coupling resistance value had inverse effects on the amount of current arriving and on the impedance of the neurite. We propose that by modulating the amplitude of EPSPs, electrical synapses could regulate the firing frequency of neurons. Abstract | Full Text | PDF (468 kb)

• A Modified Cable Formalism for Modeling Neuronal Membranes a...

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• Frequency domain analysis of electrotonic coupling between l...

  Frequency domain analysis of electrotonic coupling between leech Retzius cells Biophysical Journal, Volume 44, Issue 1, 1 October 1983, Pages 91-99 J. Yang and K.M. Chapman Abstract Transfer functions of the input impedance Z(f) and coupling ratio H(f) were measured from the paired Retzius cells of leech segmental ganglia, using sinusoidal and pseudorandom test test currents. The data were compared with two classes of linear electric circuit models of electrotonic coupling, one with a purely resistive junction, and the other with a finite equivalent cable coupling the two somata. Model simulations suggested the phase behavior of the coupling ratio as a sensitive discriminator between these two cases. For resistive coupling, the phase of the coupling ratio asymptotically approaches -90 degrees at high frequencies, while for a cable segment, at least 0.5 length constants in length, it crosses -90 degrees with a definite negative slope and continues to more negative values. Measured phase lags of the coupling ratio in Retzius cell preparations consistently exceeded -90 degrees at frequencies above 50 Hz, and phase plots crossed -90 degrees with significantly negative slopes. We conclude therefore that a significant cable segment contributes to the coupling between Retzius cell somata. Abstract | PDF (944 kb)

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Abstract

The cable equation is solved in the Laplace transform domain for arbitrary initial and boundary conditions. The cable potential is expressed directly in terms of the impedance of the terminations and the cable electrotonic length. A computer program is given to invert the transform. Numerical solutions may be obtained for any particular model by inserting expressions describing the terminations and parameter values into the program, without further computation by the modeler. For a finite length cable, sealed at one end, the solution is expressed in terms of the ratio of the termination impedance to the impedance of the finite length cable, a generalization of the steady-state conductance ratio. Analysis of a model of a soma with several primary dendrites shows that the dendrites may be lumped into one equivalent cylinder if they have the same electrotonic length, even though they may vary in diameter. Responses obtained under voltage clamp are conceptually predictable from measurements made under current clamp, and vice versa. The equalizing time constants of an infinite series expression of the solution are the negative reciprocals of the roots of the characteristic equation. Examination of computed solutions shows that solutions which differ theoretically may be indistinguishable experimentally.